What Is The Square Root Of 144?

You are here to get the answer to the question of what is the Square Root Of 144, let us see how it is calculated. The Square of a number is a number that when multiplied by itself is equal to the first number. The number 144 square root will be a number which when multiplied by itself gives you the answer 144. Let us see about the Square Root Of 144.

What Is The Square Root Of 144?

The Square Root Of 144 in radical form is written as √144 and the answer to the square root of 144 is 12.

Square Root Of 144

√144 = 12

Square Root Of 144 In Exponential Form

√144 = (144)½

Square Root Of 144 In Radical Form

√144 = √144

How To Find The Square Root Of 144?

To find the square root of 144 there are 2 methods.

Prime Factorization
Long Division Method

Let us find out the square root of 144 by both methods

Prime Factorization

To get the answer to the square root for 144 through the radical form method is very simple.

Now as 144 is a prime number so

144 = 2×72
144 = 2x2x36
144 = 2x2x2x18
144 = 2x2x2x2x9
144 = 2x2x2x2x3x3

So,

√144 = √2x2x2x2x3x3

√144 = √(2x2x3)²

√144 = √(12)²

√144 = 12

Therefore, the answer for √144 = 12

Long Division Method

The Square Root Of 144 in long division method is done in these steps

To find the square root of 144 using the long division method, follow these steps:

Step 1:

Write the numbers on the right side we will put a bar above it

Step 2:

Write such number on the left side that when we multiplied by itself you get a number that is either <=144. Here you need to write 12 as the divisor and 12 as the quotient when multiplied 12 by 12 you get 144 and the remainder will be 0.

Your quotient is 12 And your divisor is 12 and the remainder is 0 as you have got your remainder as 0 it cannot be further divided.

So the square root of 144 is 12

Is the Square Root Of 144 Rational or Irrational?

The Square Root Of 144 is a rational number.

As there is the number 12 that when multiplied by itself will give you the answer 144 so it is a perfect square so this number is a rational number.

Also, the square root of 144 is 12 which gives you a remainder of 0.

So √144 is a rational number

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FAQ

What Is The Exact Square Root Of 144?

The exact square root of 144 is 12 as you know that 12 x 12 = 144.

How Do You Simplify √144?

The Simplified form of √144 = 12

By prime factorization

144 = 2×72 = 2x2x36 = 2x2x2x18 = 2x2x2x2x9 = 2x2x2x2x3x3

So, √144 = √2x2x2x2x3x3 = √(2x2x3)² = √(12)² = 12

Therefore, the answer for √144 = 12

Why Is 12 The Square Root Of 144?

12 is the square root of 144 because

144 = 2×72 = 2x2x36 = 2x2x2x18 = 2x2x2x2x9 = 2x2x2x2x3x3

So, √144 = √2x2x2x2x3x3 = √(2x2x3)² = √(12)² = 12

Therefore, the answer for √144 = 12

Is 144 A Perfect Square?

Yes, Is 144 a perfect square because 12 x 12 is 144 and any number that is resulted by multiplying a number by itself is a perfect square.

Why Is 144 A Special Number?

144 is the square of 12. It is also the twelfth Fibonacci number, following 89 and preceding 233, and the only Fibonacci number (other than 0, and 1) to also be a square. 144 is the smallest number with exactly 15 divisors, but it is not highly composite since the smaller number 120 contains 16.

Conclusion

So 12 is the Square Root Of 144 and you can calculate the root of 144 by 2 methods which are the prime factorization & Long Division Method. After understanding the methods mentioned above you can easily find the Square Root Of 144.